Free-Variable Tableaux for Propositional Modal Logics

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.     

Effects of nitric oxide inhibition on avoidance learning in the chick are lateralized and localized

Bilateral administration of nitric oxide synthase inhibitors into the intermediate medial hyperstriatal (IMHV) region of the chick brain impairs memory formation for an avoidance task. The aim of the current study was to determine whether this effect was restricted to a particular location in the brain, and whether inhibition was equally effective in both hemispheres. White Leghorn x black Australorp chicks were administered 0.5 mM N(omega)-Nitro-L-arginine methyl ester bilaterally into the lobus parolfactorius (LPO), or unilaterally into the IMHV. Injections into the LPO between 5 min pre-training and 40 min post-training had no effect on retention. In contrast, unilateral injections into the IMHV impaired retention and memory loss occurred from 40 min post-training. The effective administration time was hemisphere-dependent, requiring left hemisphere administration around the time of training and right hemisphere administration between 15 and 25 min post-training. These data suggest that localized nitric oxide activity in each hemisphere of the chick brain is necessary for the consolidation of memory for this task.     

What does an intermediate success rate mean? An analysis of a Piagetian liquid conservation task in the great apes

The study investigates what an intermediate success rate means in bonobos, chimpanzees, and orangutans. Apes participated in liquid conservation experiments where they had to track the larger of two different quantities of juice after various kinds of transformations [Suda, C., & Call, J. (2004). Piagetian liquid conservation in the great apes (Pan paniscus, Pan troglodytes, and Pongo pygmaeus). Journal of Comparative Psychology, 118, 265-279). When making a decision, apes sometimes demonstrated hesitant behavior, concurrently pointing to both alternatives or successively changing their choice. Moderately successful apes showed more hesitation than highly successful or unsuccessful apes. The results are consistent with the cognitive conflict model: The experiments created a higher degree of cognitive conflict on moderately successful apes than on very successful or unsuccessful apes. This indicates that an intermediate performance reflects the joint operation and potential conflict between two different cognitive strategies (identity and appearance) inherent to the Piagetian conservation task.     

Synchronization of Logics

Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction systems and provide a categorial characterization of the construction. We illustrate the technique in two cases: linear temporal logic versus equational logic; and linear temporal logic versus branching temporal logic. Finally, we lift the synchronization on formulae to the category of logics over consequences systems.     

Interpolation and Amalgamation; Pushing the Limits. Part I

Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open.Related issues of universal algebra and of algebraic logic are discussed, too. In particular we investigate the possibility of extending the characterization of interpolability to arbitrary algebraizable logics.